Everything will boil down to an individual's circumstance when trying to ascertain which best works and has the most benefits -- driving or using the country's various public transportation systems.
The daily situation of taking kids to school and picking them up is common among average American families. If this is your family's situation, then it would be pointless trying to access public transportation. You will have more peace of mind knowing that your kids will at least be safer with you behind the wheel and you get to see them everyday get past the gates to the safety and security of their respective school campuses. Unless of course your children are way past their elementary schooling days, and would probably not appreciate being driven to and from school as their friends might tease them, then yes, you can go ahead and set aside loose change every morning for your kids' bus fares.
If you have been driving a car ever since you can remember, but are quite fed up of paying such high fuel prices, then it might be worthwhile to hit the bus stop or train station every now and then to try and take advantage of the more affordable yet reliable public transport system. Not only will you help your budget by cutting down on your fuel costs and daily parking meter fees, but also do your share in minimizing the greenhouses gases that are emitted into the air. What's best, you get to take advantage of the incentive program most car insurance providers offer their clients who decide to use their vehicles less often.
Stress brought about by going to and from work or school is another consideration. Public transportation systems can be packed, especially during rush hour. But that is not saying that the streets are less crowded. This is especially true with highly urbanized areas notorious for their crowded streets.
In the end, the answer will all depend on you. But if the issue has been bugging you, then it might be good to strike a balance between the two options. Why not try minimizing the number of days you drive your car to work? If you do this, it will be a win-win situation for all. Not only will you get to save a bundle, but also get to support the local public transport system thus indirectly help people employed in the industry. And best most of all you get to help give the Earth a breather for not sucking in your car's fumes every single day.